In U.S. patent application Ser. No. 08/565,804 a technique has been described for embedding digital data in images that can be implemented either digitally or optically. This technique is aimed at satisfying the requirements that it will not visibly distort the image, it is not easily corrupted by the image content or defects, and that it is robust to basic image processing tasks such as filtering, cropping, rotation, resizing, or compression.
This technique of embedding digital message data in a source image includes the steps of: a) generating a multi-level message data image representing the digital message data; b) convolving the multi-level message data image with an encoding carrier image to produce a scrambled message data image; and c) adding the scrambled message data image to the source image to produce a source image containing embedded data. The message data is recovered from the source image containing embedded image data by: a) cross correlating the source image containing embedded data with a decoding carrier image to recover the message data image; and b) extracting the digital message data from the recovered message data image.
In the above invention, the preferred carrier signal is defined as a frequency modulated (FM) sinusoid. In particular, the FM signal is modulated in a radially symmetric fashion to accommodate the possibility that the image has been rotated. Further, the frequency undulation of the carrier as a function of distance from the center of the carrier is defined as either a linear or a logarithmic undulation function, wherein the logarithmic function is the preferred undulation function due to its robustness to small image scale changes.
However, the above invention has several shortcomings. First, because the carrier signal is deterministic, it is conceivable that a user of the images produced by the method of U.S. patent application Ser. No. 08/565,804 may deduce the carrier undulation function used in the data hiding process. Once the carrier function is understood it may be possible to subtract out the embedded data from the image. This is particularly a disadvantage when one intent of the process is to embed copyright or other secret messages.
Additionally, in the afore referenced patent application, it can be shown that the frequency amplitude spectrum of the carrier is not constant. As a result, the autocorrelation function of the frequency modulated (FM) sinusoid is not a delta function and has strong sidelobes. This has a negative influence on the quality of the extracted message data. In fact, as explained in that patent application, optimum data extraction is achieved only if the autocorrelation function of the carrier signal is an exact delta function.